Theoretical Foundations Of Deep Learning

This book offers a comprehensive exploration of the theoretical foundations of deep learning, bridging the gap between its ever increasing empirical success and rigorous mathematical understanding. With a focus on interdisciplinary approaches, it illuminates the interplay between mathematics, statistics, and computer science to address pressing challenges in deep learning research. While deep learning continues to revolutionize industries such as healthcare, gaming, and autonomous systems, its applications in solving mathematical problems like inverse problems and partial differential equations mark a paradigm shift in scientific inquiry. Yet, this rapid progress often outpaces our theoretical understanding, leaving critical questions about expressivity, optimization, robustness, and fairness unanswered.This book aims to close this gap by presenting perspectives from mathematics, statistics, and applications. This interdisciplinary endeavor draws upon diverse mathematical...